Finite Group Databasebeta

← C2×#22592023 #32166104

Subgroups — C2×#22592023 #32166104

Order 18176.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556106C211yesmaximal, characteristic
2C22×#14556085C211yesmaximal, characteristic
3#22592023C2116yesmaximal, direct product factor
4C2×#17985937C211yesmaximal, characteristic, complemented
5C2×#17985930C211yesmaximal, characteristic, complemented
6C2×#17985929C211yesmaximal, characteristic, complemented
7C2×#17985919C211yesmaximal, characteristic, complemented
8C2×#17985903C211yesmaximal, characteristic, complemented
9C2×#17985883C211yesmaximal, characteristic, complemented
10C2×#17985882C211yesmaximal, characteristic, complemented
11C2×#17985870C211yesmaximal, characteristic
12C2×#17985870C211yesmaximal, characteristic
13C2×#17985861C211yesmaximal, characteristic
14C2×#17985856C211yesmaximal, characteristic
15C2×#95×D71C211yesmaximal, characteristic
16C2×#389×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556106—28no—
22C2×#14556106C2218yes—
23C2×#14556085—28no—
24C2×#14556085C2218yes—
25C22×C4⋊Dic71C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985937C2218yescomplemented
38#17985930C2218yescomplemented
39#17985929C2218yescomplemented
40#17985919C2218yescomplemented
41#17985903C2218yescomplemented
42#17985883C2218yescomplemented
43#17985882C2218yescomplemented
44#17985870C2218yes—
45#17985870C2218yes—
46#17985861C2218yes—
47#17985856C2218yes—
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60#95×D71C2218yes—
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66#389×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142—42no—
73C22×Dic142C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—42no—
88C22×C4×D71—42no—
89C22×C4×D71Q818yescomplemented
90C22×C4×D71C2314yes—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93#14556106—232no—
94#14556085—232no—
95C2×C4⋊Dic71—24no—
96C2×C4⋊Dic71C2314yes—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—42no—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4D418yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×C4×Dic71—24no—
118C2×C4×Dic71C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71—24no—
139C2×C4⋊C4×C71—24no—
140C2×C4⋊C4×C71—42no—
141C2×C4⋊C4×C71—42no—
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C42×C71—24no—
147C2×C42×C71C2314yes—
148#95×C71C2314yes—
149#95×C71C2314yes—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71C2×D414yes—
155C23×D71C2×Q814yes—
156C23×D71#4114yes—
157C23×D71C2412yes—
158C2×Dic142—28no—
159C2×Dic142—28no—
160C2×Dic142—44no—
161C2×Dic142—416no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71C2×D414yes—
181C22×Dic71C2×Q814yes—
182C22×Dic71#4114yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C2×C4×D71—232no—
191C2×C4×D71—28no—
192C2×C4×D71—28no—
193C2×C4×D71—28no—
194C2×C4×D71—28no—
195C2×C4×D71—28no—
196C2×C4×D71—28no—
197C2×C4×D71—44no—
198C2×C4×D71—44no—
199C2×C4×D71—416no—
200C2×C4×D71—416no—
201C2×C4×D71C2×Q8116yescomplemented
202C4⋊Dic71—28no—
203Dic71⋊C4—28no—
204Dic71⋊C4—28no—
205Dic71⋊C4—28no—
206Dic71⋊C4—28no—
207Dic71⋊C4—28no—
208Dic71⋊C4—44no—
209(C2×D71)⋊C4—28no—
210(C2×D71)⋊C4—28no—
211(C2×D71)⋊C4—28no—
212(C2×D71)⋊C4C2×D4116yes—
213C4×Dic71—28no—
214C24×C71C2411yescharacteristic
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71C2×D414yes—
234C22×C4×C71C2×Q814yes—
235C22×C4×C71#4114yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C4⋊C4×C71—28no—
244C4⋊C4×C71—28no—
245C4⋊C4×C71—44no—
246C4⋊C4×C71—44no—
247C42×C71—28no—
248C23×C71C22×D412yes—
249C23×C71C22×Q812yes—
250C23×C71C2×#4112yes—
251C23×C71C2×#4112yes—
252C23×C71C2×#4112yes—
253C23×C71H(5,𝔽2)12yes—
254C23×C712−1+412yes—
255C23×C71C2511yescharacteristic
256C22×D71—28no—
257C22×D71—28no—
258C22×D71—28no—
259C22×D71—28no—
260C22×D71—28no—
261C22×D71—28no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71C22⋊Q8116yes—
267C22×D71C22×D414yes—
268C22×D71C22×Q814yes—
269C22×D71C2×#4114yes—
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—28no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—44no—
292C2×C4×C71—44no—
293C2×C4×C71—44no—
294C2×C4×C71—44no—
295C2×C4×C71C22×D414yes—
296C2×C4×C71C22×Q814yes—
297C2×C4×C71C2×#4114yes—
298C2×Dic71—28no—
299C2×Dic71—28no—
300C2×Dic71—28no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—44no—
320C2×Dic71—44no—
321C2×Dic71—44no—
322C2×Dic71—44no—
323C2×Dic71C22×D414yes—
324C2×Dic71C22×Q814yes—
325C2×Dic71C2×#4114yes—
326C4×D71—232no—
327C4×D71—416no—
328C4×D71—416no—
329Dic142—416no—
330C22×C71C2×C22⋊Q814yes—
331C22×C71#53314yes—
332C22×C71#54414yes—
333C22×C71#54614yes—
334C22×C71#54714yes—
335C22×C71#55114yes—
336C22×C71#55214yes—
337C22×C71C23×D411yescharacteristic
338C22×C71C23×Q811yescharacteristic
339C22×C71C22×#4111yescharacteristic
340C22×C71C22×#4111yescharacteristic
341C22×C71C22×#4111yescharacteristic
342C22×C71C2×H(5,𝔽2)11yescharacteristic
343C22×C71C2×2−1+411yescharacteristic
344C2×D71—24no—
345C2×D71—24no—
346C2×D71—232no—
347C2×D71—24no—
348C2×D71—24no—
349C2×D71—24no—
350C2×D71—24no—
351C2×D71C2×C22⋊Q818yes—
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—24no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71—42no—
359Dic71—24no—
360Dic71—24no—
361Dic71—24no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365Dic71—42no—
366C2×#2438—711nomaximal, Sylow
367C2×C71#243818yescomplemented
368C2×C71C22×C22⋊Q811yescharacteristic
369C2×C71C2×#53311yescharacteristic
370C2×C71C2×#54411yescharacteristic
371C2×C71C2×#54611yescharacteristic
372C2×C71C2×#54711yescharacteristic
373C2×C71C2×#55111yescharacteristic
374C2×C71C2×#55211yescharacteristic
375D71—28no—
376C22×C22⋊Q8—711no—
377C22×#117—711no—
378#2438—7116no—
379C2×#400—711no—
380C2×#398—711no—
381C2×#398—711no—
382C2×#395—711no—
383C2×#391—711no—
384C2×#389D7111yescharacteristic, complemented
385C2×#387—711no—
386C2×#387—711no—
387C2×#385—711no—
388C2×#385—711no—
389C2×#381—711no—
390C2×#380—711no—
391C22×#95—711no—
392C71C2×#243811yescharacteristic, complemented, Sylow
393C23×Q8—711no—
394C24×C4—711no—
395C24×C4—711no—
396C24×C4—711no—
397C2×C22⋊Q8—718no—
398C2×C22⋊Q8—1428no—
399C2×#117—718no—
400C2×#117—1428no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—711no—
408C22×C4⋊C4C2×D7111yescharacteristic
409C22×C4⋊C4C2×D7111yescharacteristic
410C22×C4⋊C4C2×D7111yescharacteristic
411C22×C4⋊C4C2×D7111yescharacteristic
412C22×C22⋊C4—711no—
413C22×C22⋊C4—711no—
414C22×C22⋊C4—711no—
415C22×C22⋊C4—711no—
416C22×C42—711no—
417C22×C42C2×D7111yescharacteristic
418#400—718no—
419#398—718no—
420#398—718no—
421#395—718no—
422#391—718no—
423#389C2×D7118yescomplemented
424#387—718no—
425#387—718no—
426#385—718no—
427#385—718no—
428#381—718no—
429#380—718no—
430C2×#95—711no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—711no—
439C2×#95—711no—
440C2×#95—711no—
441C2×#95—711no—
442C2×#95—718no—
443C2×#95C2×D7111yescharacteristic
444C2×#95C2×D7111yescharacteristic
445C25—711no—
446C22×Q8—2842no—
447C22×Q8—714no—
448C22×Q8—1424no—
449C22×Q8—1424no—
450C23×C4—2842no—
451C23×C4—2842no—
452C23×C4—714no—
453C23×C4—714no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—718no—
458C23×C4—714no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—1424no—
464C23×C4—1424no—
465C23×C4—1424no—
466C23×C4—1424no—
467C23×C4—1424no—
468C23×C4—1424no—
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7111yescharacteristic
474C23×C4C22×D7111yescharacteristic
475C23×C4C22×D7111yescharacteristic
476C22⋊Q8—14232no—
477#117—14232no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—2842no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—714no—
485C2×C4⋊C4—714no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—714no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4—714no—
490C2×C4⋊C4—1424no—
491C2×C4⋊C4—1424no—
492C2×C4⋊C4—1424no—
493C2×C4⋊C4—1424no—
494C2×C4⋊C4—1424no—
495C2×C4⋊C4—1424no—
496C2×C4⋊C4C22×D7114yes—
497C2×C4⋊C4C22×D7114yes—
498C2×C4⋊C4C22×D7114yes—
499C2×C4⋊C4C22×D7114yes—
500C2×C22⋊C4—718no—
501C2×C22⋊C4—714no—
502C2×C22⋊C4—714no—
503C2×C22⋊C4—714no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—1424no—
506C2×C22⋊C4—1424no—
507C2×C22⋊C4—1424no—
508C2×C42—24no—
509C2×C42—714no—
510C2×C42—1424no—
511C2×C42C22×D7114yes—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95C22×D7114yes—
525#95C22×D7114yes—
526C24—714no—
527C24—714no—
528C24—714no—
529C24—712no—
530C24—1422no—
531C24—1422no—
532C24—1422no—
533C24—1422no—
534C24C23×D7111yescharacteristic
535C2×Q8—2844no—
536C2×Q8—28416no—
537C2×Q8—1428no—
538C2×Q8—1428no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—28416no—
558C22×C4—2844no—
559C22×C4—2844no—
560C22×C4—28416no—
561C22×C4—714no—
562C22×C4—714no—
563C22×C4—714no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—712no—
567C22×C4—7116no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—712no—
572C22×C4—1428no—
573C22×C4—1428no—
574C22×C4—1428no—
575C22×C4—1428no—
576C22×C4—1428no—
577C22×C4—14232no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1428no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4D4×D7114yes—
598C22×C4Q8×D7114yes—
599C22×C4#1176586514yes—
600C22×C4C23×D7112yes—
601C22×C4C23×D7112yes—
602C22×C4C23×D7112yes—
603C22×C4C23×D7112yes—
604C22×C4C23×D7112yes—
605C22×C4C23×D7112yes—
606C22×C4C23×D7112yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—2844no—
612C4⋊C4—1428no—
613C4⋊C4—1428no—
614C4⋊C4—1428no—
615C4⋊C4—1428no—
616C4⋊C4—1428no—
617C4⋊C4—1428no—
618C22⋊C4—7116no—
619C22⋊C4—1428no—
620C22⋊C4—1428no—
621C22⋊C4—1428no—
622C42—28no—
623C42—1428no—
624C23—714no—
625C23—714no—
626C23—714no—
627C23—7116no—
628C23—1422no—
629C23—1422no—
630C23—1422no—
631C23—1422no—
632C23—1428no—
633C23—1428no—
634C23—1428no—
635C23—1428no—
636C23—1428no—
637C23—1428no—
638C23C2×D4×D7112yes—
639C23C2×Q8×D7112yes—
640C23#41×D7112yes—
641C23#41×D7112yes—
642C23C2×#1176586512yes—
643C23#1455617312yes—
644C23#1455617612yes—
645C23C24×D7111yescharacteristic
646Q8—28416no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—28416no—
673C2×C4—28416no—
674C2×C4—2844no—
675C2×C4—2844no—
676C2×C4—2844no—
677C2×C4—2844no—
678C2×C4—714no—
679C2×C4—714no—
680C2×C4—714no—
681C2×C4—14232no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1422no—
698C2×C4—1422no—
699C2×C4—1422no—
700C2×C4—1428no—
701C2×C4—1428no—
702C2×C4—1428no—
703C2×C4C2×D4×D7114yes—
704C2×C4C2×Q8×D7114yes—
705C2×C4C2×#1176586514yes—
706C22—718no—
707C22—1424no—
708C22—14232no—
709C22—1424no—
710C22—1424no—
711C22—1424no—
712C22—1424no—
713C22—1424no—
714C22C22⋊Q8×D7114yes—
715C22#1798655314yes—
716C22#1798662614yes—
717C22#1798664614yes—
718C22#1798665014yes—
719C22#1798667814yes—
720C22#1798668114yes—
721C22C22×D4×D7111yescharacteristic
722C22C22×Q8×D7111yescharacteristic
723C22C2×#41×D7111yescharacteristic
724C22C2×#41×D7111yescharacteristic
725C22C22×#1176586511yescharacteristic
726C22C2×#1455617311yescharacteristic
727C22C2×#1455617611yescharacteristic
728C4—24no—
729C4—24no—
730C4—24no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2842no—
736C4—2842no—
737C4—2842no—
738C4—2842no—
739C4—1424no—
740C4—1424no—
741C4—1424no—
742C2—1428no—
743C2#2259202318yesdirect product factor
744C2C2×C22⋊Q8×D7111yescharacteristic
745C2C2×#1798655311yescharacteristic
746C2C2×#1798662611yescharacteristic
747C2C2×#1798664611yescharacteristic
748C2C2×#1798665011yescharacteristic
749C2C2×#1798667811yescharacteristic
750C2C2×#1798668111yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#389×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#389D71
hypocenterC71C2×#2438
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #22592023C2direct (N × H)
4. C2×#17985937C2semidirect
5. C2×#17985930C2semidirect
6. C2×#17985929C2semidirect
7. C2×#17985919C2semidirect
8. C2×#17985903C2semidirect
9. C2×#17985883C2semidirect
10. C2×#17985882C2semidirect
16. C2×#389×C71C2semidirect
37. #17985937C22semidirect
38. #17985930C22semidirect
39. #17985929C22semidirect
40. #17985919C22semidirect
41. #17985903C22semidirect
42. #17985883C22semidirect
43. #17985882C22semidirect
66. #389×C71C22semidirect
89. C22×C4×D71Q8semidirect
201. C2×C4×D71C2×Q8semidirect
367. C2×C71#2438semidirect
384. C2×#389D71semidirect
392. C71C2×#2438semidirect
423. #389C2×D71semidirect
743. C2#22592023direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145561062
C22×#145560852
#225920232
C2×#179859372
C2×#179859302
C2×#179859292
C2×#179859192
C2×#179859032
C2×#179858832
C2×#179858822
C2×#179858702
C2×#179858612
C2×#179858562
C2×#95×D712
C2×#389×C712
C2×#243871